Question

If sin²(10°)sin(20°)sin(40°)sin(50°)sin(70°) = α – 1/16 sin(10°), then 16 + α^–1 is equal to __________.

Answer 1

Answer is 80

= 1/32(2sin10° cos20° sin10°)

= 1/32(sin 30° sin10° sin10°) 

= 1/32 (1/2 - 2 sin 10°) 

= 1/64 (1 - 4 sin 10°) 

Hence α = 1/64

16 + α^-1 = 80

Comments

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